Meinrenken's proof of the existence of groupoid tubular neighborhoods for proper Lie groupoids is based on the existence of Euler-like multiplicative vector fields [1]}. Namely, a vector field on a manifold \(M\)  is called Euler-like with respect to a submanifold \(C\)  if it vanishes along the submanifold and its linear approximation is the Euler vector field \(\mathcal {E}\)  on the normal bundle \(\nu (C)\) , i.e. \(\mathcal {E}\)  is the vector field having scalar multiplication by \(e^{-t}\)  as its flow at the normal direction. It is important to mention that an Euler-like vector field \(X\)  for \((M,C)\)  determines a unique maximal tubular neighborhood embedding \(\phi :\nu (C)\rightarrow M\)  such that \(\phi ^* X=\mathcal {E}\) ; compare with [2]}.
